{
  "abstract": "We study commutators $[(-Δ_θ)^{\\fracε{2}},M_x]$ involving fractional Laplacians on quantum Euclidean spaces associated with arbitrary real antisymmetric matrices $θ$. For $d\\geq2$ and $-\\frac d2<ε\\neq 0<1$, we characterize critical weak Schatten class membership of $[(-Δ_θ)^{\\fracε{2}},M_x]$ for any $x$ as a tempered distribution by Sobolev spaces, with equivalent corresponding norms. We also establish precise asymptotics of singular values for $[(-Δ_θ)^{\\fracε{2}},M_x]$. For this purpose, we extend the Cwikel estimates and the required asymptotics of singular values to arbitrary real antisymmetric matrices, and we also establish a systematic approximation theory of tempered distributions on quantum Euclidean spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06405",
  "author_total": 3,
  "authors": [
    {
      "name": "Changbao Pang"
    },
    {
      "name": "Maofa Wang"
    },
    {
      "name": "Hao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eazavbekz4sr1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06405",
  "fulltext_url": null,
  "id": "eazavbekz4sr1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06405",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06405",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eazavbekz4sr1.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06405",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06405"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Endpoint Schatten class properties of commutators on quantum Euclidean spaces",
  "title_text": "Endpoint Schatten class properties of commutators on quantum Euclidean spaces",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/eazavbekz4sr1",
  "venue": "arXiv",
  "versions": []
}